Question

Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question. A jar contains 70 nickels and dimes worth $6.10. How many of each kind of coin are in the jar? nickels dimes

Answer 1

There are 18 nickels and 52 dimes in the jar

Explanation:

First establish the variables of x and y

x = number of nickels.

y = numer of dimes.

Then develope the system of two linear equations with two variables.

The first equation can result from adding the number of nickels and dimes which result will be 70 coins then

x + y = 70

The second equation is related with the value, so if we multiply the number of nickels by its value and add it with the number of dimes by its value we will have $6.10 then we have:

0.05x + 0.1y = 6.10

Now we have the two equations and we are going to solve them by the elimination method

x + y = 70

0.05x + 0.1y = 6.10

We are going to eliminate x then we have to multiply by -0.05 in both sides of the first equation and we are going to leave the second equation the same but in the first line to make easier the process.

0.05x + 0.1y = 6.10

(x+y)(-0.05) = 70*(-0.05)

0.05x + 0.1y = 6.10

-0.05x -0.05y = -3.50 (now do the operation)

0 +0.05y = 2.60

y =
`(2.60)/(0.05\\)`

y = 52

We have 52 dimes.

Now replace in the initial equation the y value

x + 52 = 70

x = 70 - 52

x = 18

We have 18 nickels

Then in the jar we have 52 dimes and 18 nickels